Module 2 Fundamental data analysis_checked

Question 1

What two types of errors are uncertainties caused by?

Answer 1

Random and systematic

Question 2

1. What are systematic errors?
2. How are they caused?
3. How easy are they to spot?
4. What is their effect?

Answer 2

1. Systematic errors [including zero errors] are the same every time you repeat the experiment, They shift all the values by the same amount.
2. They may be caused by the equipment you’re using or how it’s set up e.g. you’re not lining up a ruler correctly when measuring extension the of a spring.
3. Systematic errors are really hard to spot.
4. Systematic errors affect the accuracy of your results. It is always worth checking your apparatus at the start of an experiment e.g. measure a few known masses to check that a mass meter is calibrated properly.

Question 3

Describe random errors. How can you reduce their effect?

Answer 3

Random errors make the results a bit different each time you repeat an experiment. If you measured the length 20 times, the chances are you’d get a slightly different value each time e/g/ due to your head being in a slightly different position when reading the scale. It could be that you just can’t keep controlled variables exactly the same throughout the experiment.

Repeating measurements can also reduce the effects of random errors. Using equipment with a higher resolution means that the equipment can detect smaller changes. This can reduce random error and make the results more precise.

Question 4

How do you find the uncertainty in the value of the gradient of a graph?

Answer 4

The uncertainty in the gradient is given by the difference between the best gradient and the worst gradient.

An alternative method using gradients is:

Uncertainty = [max gradient - min gradient] / 2

Question 5

How do you find the uncertainty in the y-intercept of a graph?

Answer 5

Draw the worst lines through the uncertainty bars. The uncertainty is the difference between the best and worst intercepts vertically for an uncertainty bar

Question 6

How do you calculate the angle of a circle arc in radians?

Answer 6

angle (in radians) = arc length (in m) / radius (in m)
think L = r * (theta)

L=rθ

Question 7

How do you calculate percentage uncertainty?

Answer 7

% uncertainty = [abs uncertainty in reading/ actual reading] * 100%

Question 8

How do you calculate uncertainties when adding or subtracting quantities

Answer 8

When adding or subtracting quantities, you add the absolute uncertainties

Question 9

1. How do you calculate percentage uncertainty when multiplying or dividing quantities,
2. How to use this to find absolute uncertainty

Answer 9

1. When multiplying or dividing quantities you add the percentage uncertainties
2. Multiply the final %uncertainty by the final quantity value to find its absolute uncertainty

Question 10

1. How do you calculate percentage uncertainty when raising a quantity to a power
2. How do you calculate absolute uncertainty from that?

Answer 10

1. When you a raise a quantity to a power, n, you multiply the % uncertainty of that quantity by n,
2. Multiply the final %uncertainty by the final quantity value to find its absolute uncertainty

Question 11

How do you calculate spread from range?

Answer 11

spread = 0.5 * range
spread is the uncertainty in a reading.

When working with dot plots be careful of anomalous values

Question 12

What is the line of worst fit and how do you calculate it?

Answer 12

This is essentially the maximum gradient or the minimum gradient.

This is the least acceptable straight line through the data points. after you have drawn your uncertainty bars at each point. Start from the bottom of the first uncertainty bar and get to top of the last uncertainty bar i.e. the maximum or minimum gradient